# Barycenters of Natural Images -- Constrained Wasserstein Barycenters for Image Morphing

arXiv: https://arxiv.org/abs/1912.11545 · HTML: https://mlsanity.com/paper/1912.11545/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2019.

## Built on by (most cited first, 11 of 11)

- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Models](https://mlsanity.com/paper/2311.06792/) (2023)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [Fixed Support Tree-Sliced Wasserstein Barycenter](https://mlsanity.com/paper/2109.03431/) (2021)
- [Probability Density Geodesics in Image Diffusion Latent Space](https://mlsanity.com/paper/2504.06675/) (2025)
- [Multiview Regenerative Morphing with Dual Flows](https://mlsanity.com/paper/2208.01287/) (2022)
- [Continual Learning of Generative Models with Limited Data: From Wasserstein-1 Barycenter to Adaptive Coalescence](https://mlsanity.com/paper/2101.09225/) (2021)
- [Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernels](https://mlsanity.com/paper/2212.01310/) (2022)
- [BlendGAN: Learning and Blending the Internal Distributions of Single Images by Spatial Image-Identity Conditioning](https://mlsanity.com/paper/2212.01589/) (2022)
- [Joint Manifold Learning and Optimal Transport for Dynamic Imaging](https://mlsanity.com/paper/2505.11913/) (2025)
- [On Barycenter Computation: Semi-Unbalanced Optimal Transport-based Method on Gaussians](https://mlsanity.com/paper/2410.08117/) (2024)

## Abstract (arXiv)

Image interpolation, or image morphing, refers to a visual transition between two (or more) input images. For such a transition to look visually appealing, its desirable properties are (i) to be smooth; (ii) to apply the minimal required change in the image; and (iii) to seem "real", avoiding unnatural artifacts in each image in the transition. To obtain a smooth and straightforward transition, one may adopt the well-known Wasserstein Barycenter Problem (WBP). While this approach guarantees minimal changes under the Wasserstein metric, the resulting images might seem unnatural. In this work, we propose a novel approach for image morphing that possesses all three desired properties. To this end, we define a constrained variant of the WBP that enforces the intermediate images to satisfy an image prior. We describe an algorithm that solves this problem and demonstrate it using the sparse prior and generative adversarial networks.